Parametric Equation of all Forms of Parabola

Here you will learn what is the parametric equation of all forms of parabola and their parametric coordinates.

Let’s begin –

Parametric Equation of Parabola and Coordinates

(i) For the parabola $y^2$ = 4ax :

The parametric equation is x = $at^2$ & y = 2at.

And parametric coordinates are ($at^2$, 2at).

(ii) For the parabola $y^2$ = -4ax :

The parametric equation is x = $-at^2$ & y = 2at.

And parametric coordinates are ($-at^2$, 2at).

(iii) For the parabola $x^2$ = 4ay :

The parametric equation is x = 2at & y = $at^2$.

And parametric coordinates are (2at, $at^2$).

Also Read : Different Types of Parabola Equations

(iv) For the parabola $x^2$ = -4ay :

The parametric equation is x = 2at & y = $-at^2$.

And parametric coordinates are (2at, -$at^2$).

(v) For the parabola $(y – k)^2$ = 4a(x – h) :

The parametric equation is x = $h + at^2$ & y = k + 2at.

And parametric coordinates are ($h + at^2$, k + 2at).

(vi) For the parabola $(x – p)^2$ = 4a(y – q) :

The parametric equation is x = p + 2at & y = $q + at^2$.

And parametric coordinates are (p + 2at, $q + at^2$).